<p>As long as he/she has had the core classes you could go to grad school in CS/EE as a mechE undergrad. It will typically be around 4 courses (for CS, it would be something like an advanced programming course, discrete structures (math), computer organization (CS/EE), and maybe operating systems. For EE it would probably be analog circuits, signal processing, digital design, and then one or two upper-level courses in whatever it is you want to study. At least here (I'm not sure about Columbia), every undergrad engineering major has to take 2 "advisor-approved" electives that can be anything and 3 technical electives outside of his/her own major, so it is fairly easy to prepare for graduate study in another field.</p>
<p>Also, do you know what the maximum number of liberal arts courses your son could take within Columbia engineering? I'm not saying this equates to mastery in any particular subject, but I have to take 6 liberal arts courses from at least 3/6 different categories (things like behavioral analysis, historical analysis, plenty more fancy names basically breaking down "liberal arts" education into 6 categories), 2 freshman writing seminars that are offered on literally any topic and can be very informative, and then 2 free ("advisor-approved") electives. That's still 10 classes that can pretty much be on any topic that interests you outside of engineering. Is Columbia's core curriculum similar?</p>